Experimental Validation of Decentralized Affine Transformation

Abstract: This paper presents an experimental validation of decentralized affine transformation (AT) in multi-agent systems using teams of mini-quadcopters. The AT framework enables an agent team to safely navigate constrained, obstacle-rich environments while allowing aggressive changes in inter-agent distances, which are formally characterized through the decomposition of the AT transformation matrix. Without loss of generality, we focus on two-dimensional AT, formulated as a decentralized leader-follower problem. In this formulation, three leader quadcopters are positioned at the vertices of a triangle, while all follower quadcopters remain within the triangle. The leaders know the desired trajectories prescribed by the AT, whereas the followers do not. Instead, the followers infer their trajectories through local communication governed by fixed communication weights determined by the initial spatial configuration of the team. Experimental results validate the asymptotic convergence of decentralized AT and demonstrate its capability to safely guide multi-agent teams through obstacle-laden environments.